The thoughts and research of a long line of social philosophers and economists attest to the fact that the current financial crisis is just the latest in centuries of frequently occurring events. Indeed, beginning with Adam Smith in the eighteenth century, Marx, Mill, Marshall, Wicksell, Fisher, Keynes, Schumpeter, Minsky and Kindleberger have all studied the causes and consequences of financial crises which have usually been appropriately "global" in their time. While perhaps not yet generally agreed, the current truly global crisis, now hopefully in its final "resolution" stage, fits virtually perfectly the stages of crisis discussed in Kindleberger's famous book in an historical context. Usually promoted by different communities and interests in isolation: "globalization" in the form of financial imbalances between developing exporting and developed importing nations, improper regulation of macroeconomic policy and markets by governments and central banks, and greedy "Anglo Saxon" bankers developing ever more complex derivative products in search of personal and corporate profits, have all been blamed for the current situation. The truth is that these three potential causes have all contributed to the current situation and all must be addressed appropriately in its resolution. As a mathematician who has worked with the global financial services industry over the past two decades, I wish to address the third issue here.

With so much science and so many applications focused on quantitative output, mathematics plays a key role in the design and evaluation of quantitative models. While in some cases simple or standard mathematics is enough to formulate models and support theories, sometimes methods are required that are very recent or even yet to be developed.